Quant Signals: Entropy w/ Forecast

This is the first of many quantitative signals I plan to create for TV users.

Most technical analysis (TA) tools—like moving averages, oscillators, or chart patterns—are heuristic: they’re based on visually identifiable shapes, threshold crossovers, or empirically chosen rules. These methods rarely quantify the information content or structural complexity of market data. By quantifying market predictability before making a forecast, this method filters out noise and focuses your trading only during statistically favorable conditions—something traditional TA cannot objectively measure.

This MEPP-based approach is quantitative and model-free:

It comes from information theory and measures Shannon entropy rate to assess how predictable the market is at any moment.

Instead of interpreting price formations, it uses a data-compression algorithm (Lempel–Ziv) to capture hidden structure in the sequence of returns.

Forecasts are generated using a principle from statistical physics (Maximum Entropy Production), not historical chart patterns.

In short, this method measures the market's predictability BEFORE deciding a directional forecast is worth trusting. This tool is to inform TA traders on the market's current regime, whether it is smooth and predictable or it is volatile and turbulent.

Technical Introduction:
In information theory, Shannon entropy measures the uncertainty (or information content) in a sequence of data. For markets, the entropy rate captures how much new information price returns generate over time:

• Low entropy rate → price changes are more structured and predictable.
  
• High entropy rate → price changes are more random and unpredictable.
  

By discretizing recent returns into quartile-based states, this indicator:

1. Calculates the normalized entropy rate as a regime filter.
   
2. Uses MEPP to forecast the next state that maximizes entropy production.
   
3. Displays both the regime status (predictable vs chaotic) and the forecast bias (bullish/bearish) in a dashboard.
   

Measurements & How to Use Them

TLDR: HIGH ENTROPY -> information generation/market shift -> Don't trust forecast/strategy

1. H (bits/sym)

• Shannon entropy rate of the last μ discrete returns, in bits per symbol (0–2).
  
• Lower → more predictable; higher → more random.
  
• Use as a raw measure of market structure.
  

2. H_max (log₂Ω)

• Theoretical maximum entropy for Ω states. Here Ω = 4 → H_max = 2.0 bits.
  
• Reference value for normalization.
  

3. Entropy (norm)

• H / H_max, scaled between 0 and 1.
  
• < 0.5–0.6 → predictable regime; > 0.6 → chaotic regime.
  
• Main regime filter — forecasts are more reliable when below your threshold.
  

4. Regime

• Label based on Entropy (norm) vs your entThresh.
  
• LOW (predictable) = higher odds forecast will be correct.
  
• HIGH (chaotic) = forecasts less reliable.
  

5. Next State (MEPP Forecast)
Discrete return state (1–4) predicted to occur next, chosen to maximize entropy production:

1. Large Down (strong bearish)
   
2. Small Down (mild bearish)
   
3. Small Up (mild bullish)
   
4. Large Up (strong bullish)
   
5. Use as your bias direction.
   

6. Bias

Simplified label from the Next State:
States 1–2 = Bearish bias (red)
States 3–4 = Bullish bias (green)

Align strategy direction with bias only in LOW regime.